The wind turbine can be a horizontal axis wind turbine or a vertical axis wind turbine comprising a rotor with rotor blades, with N the number of rotor blades and R the blade radius. Due to rotation, the blade tip at radius R obtains a tip speed νtip equal to the product of the rotor speed ω and the rotor radius R: νtip=ωR. The undisturbed wind speed V is the wind speed at the locus of the axis of the rotor when the wind turbine does not disturb the flow. The ratio between the νtip and V is the tip speed ratio λ=ωR/V. An airfoil is a for the aerodynamics optimized profile which is round at the leading edge and sharp or cut off at the trailing edge. One side of the airfoil is the upper side or suction side, the other side is the lower side or the pressure side.
The curve through the centres of circles within the airfoil touching both the lower side and the upper side is called the camber line. At the leading edge this line continues to the airfoil contour. The line part which connects the most forward and the most backward part of the camber line is the chord c or the local chord cr at radial position r. A rotor blade may exist of several airfoils at the same radial position. In such a case the sum of the chords of the airfoils should be taken as the locale chord cr.
The leading edge of the airfoil is located at 0% of the chord (0% c) and the trailing edge at 100% c. The largest distance between the camber line and the chord is the camber. The ratio between the diameter of the largest circle in the airfoil and the chord is the thickness t of the airfoil. Flexible or in position controllable parts of the aft part of the airfoil, which can move more than 2.5% c with respect to the leading edge are not part of the chord. The lift L=½ρU2clc and drag D=½ρU2clc of an airfoil are both proportional to the chord c and respectively to the lift coefficient cl and the drag coefficient cd.
The chord follows from the equation C=M. Here in M is a dimensionless momentum loss. C is the chord number which is Nrcrclλ2/(2πR2) for a horizontal axis turbine and Nrcrclλ2/R2 for a vertical axis turbine. This number prescribes how the parameters N, cr, cl, r, R and λ should be chosen in order to realise a certain dimensionless momentum loss in the flow. Close to the axis of rotation, the chord number does not provide good values and therefore this number is primary useful in the range starting at 0.3R-0.6R and ending at 0.9R-1.0R. Example for a horizontal axis wind turbine with M=¾. When the designer chooses R=50 m, λ=8, N=3 and cl=0.9 then it follows that crr=68.2 m2, so at 25 m radial position the chord should be about 2.73 m. The average chord number in e.g. the range of 0.5R to 0.9R is:
      C    _    =            1              0.4        ⁢                                  ⁢        R              ⁢                  ∫                  r          =                      0.5            ⁢                                                  ⁢            R                                    r          =                      0.9            ⁢                                                  ⁢            R                              ⁢                                    N            ⁢                                                  ⁢            r            ⁢                                                  ⁢                          c              r                        ⁢                          c              l                        ⁢                          λ              2                                            2            ⁢                                                  ⁢            π            ⁢                                                  ⁢                          R              2                                      ⁢                                  ⁢                              ⅆ            r                    .                    
The chord of a wind turbine blade can be calculated also with the equation Ncrrλ2/R2=8πα(1−α)/cl, in which α is the axial induction according to the Lanchester-Betz theory. The term on the left hand side of the equation is the chord number D, of which the average in e.g. the range of 0.4R to 0.95R is:
      D    _    =            1              0.55        ⁢                                  ⁢        R              ⁢                  ∫                  r          =                      0.4            ⁢                                                  ⁢            R                                    r          =                      0.95            ⁢            R                              ⁢                                    N            ⁢                                                  ⁢            r            ⁢                                                  ⁢                          c              r                        ⁢                          λ              2                                            R            2                          ⁢                                  ⁢                              ⅆ            r                    .                    
The power coefficient Cp=P/(½ρAV3), in which P is the power extracted from the flow according to the Lanchester-Betz theory, ρ is the air density and A the swept area πR2. The extracted power P will be higher than the electric power Pe due to transfer losses. For values of Pe between 0.5Pnom and Pnom, in which Pnom is the nominal or rated power, it is assumed that P=1.2Pe. The pitch angle is 0° when the local chord at 0.99R is located in the plane in which the blade is rotating. The angle becomes more positive when the blade pitches towards vane position. The angle of attack is the angle between the chord and the undisturbed inflow in a 2D situation. The angle of attack at which the blade develops zero lift is the 0-lift angle. The lift (coefficient) increases approximately linear with the angle of attack for small angles of attack (e.g. between −8° and +8°). Most pitch regulated variable speed turbines operate essentially at or near constant tip speed ratio λ below rated wind speed. The turbine may deviate from this constant λ operation e.g. to avoid certain eigenfrequencies or to decrease sound emission. Still it is optimised for a certain λdesign and the airfoils operate on average at the angle of attack αdesign which gives optimum performance. At αdesign the airfoil develops a lift coefficient cl,design design and has a lift over drag ratio L/Ddesign. When actual turbines produce power under non-extreme conditions and below rated wind speed, the mean value of the angle of attack and also of the lift coefficient approach the design value. The momentary realisations of those parameters behave stochastic due to turbulence, yaw, shear etc. A common method to characterise a wind turbine is to bin parameters like the 10-minute averaged power or angle of attack or lift coefficient as a function of the 10 minute averaged wind speed. When many data points are collected in each bin and averaged a more or less accurate estimate of the averages of those parameters is obtained. The so obtained value of for example a lift coefficient at a certain wind speed is the mean lift coefficient or the 10 minute averaged lift coefficient. If the turbine is produced conform the design, those mean or 10 minute averaged values correspond to the design values. So essentially the design value, the 10 minute averaged value and the mean value of a parameter such as the lift coefficient or angle of attack are equivalent. The angle at which the airfoil stalls or the flow separates from the surface is airfoil dependent. A typical stall angle is +10°, at which the lift coefficient is about 1.0 to 1.6. At larger angles cl increases slightly or even decreases and simultaneously cd increases, so that the efficiency of the rotor blades drops.
Flow separation can be avoided with lift enhancing means, such as known in literature. Examples of such lift enhancing means are vortex generators (VGs), gurney flaps, lengthening of the chord, increase of camber, suction of the boundary layer, flaps near the leading edge or near the trailing edge, deformation of a flexible part at the trailing edge of the airfoil, application of the Magnus effect, FCS such as described in Sinha, S. K., WO03067169, synthetic jets which feed energy into the boundary layer such as is known by e.g. Gerhard, L., U.S. Pat. No. 4,674,717 and MEM translational tabs. Most of those options can be applied in a passive and an active sense, in said active case the control can be by pneumatics, hydraulics, electromagnetics, piezo electrics, by MEM translational tabs or any other control method known from literature. All those lift enhancing means can principally be attached as separate elements to the blade or can be integrated with the blade.
VGs are elements which generate vortices which feed energy into the boundary layer. VGs can be elements which are more or less submerged in the surface and are known in many different shapes. Examples are a special curvature of the airfoil surface itself (e.g. cavities) or surfaces which extend from the airfoil surface into the flow. Possible connection parts such as a base which is connected to the VG, is not counted as part as the VG. The chord position of the VG is related to the part of the VG at the smallest chord position. The base can be essentially flat or following the local airfoil shape. Known shapes of VGs can be found in Waring, J., U.S. Pat. No. 5,734,990; Kuethe, A. M., U.S. Pat. No. 3,578,264; Kabushiki, K. T., EP0845580; Grabau, P., WO00/15961; Corten, G. P., NL1012949, Gyatt, G. W., DOE/NASA/0367-1 etc. VGs may have a length of about 3% of the chord, a height of about 1% of the chord and a mutual distance of about 5% of the chord. VGs postpone stall to larger angles of attack. Airfoils with VGs reach typical lift coefficients of 1.5-2.5 at angles of attack of e.g. +12° tot +25°. Three or more VGs at regular spacing attached essentially in a line biased less than 30° from the line perpendicular to the flow direction is defined as a basis line of VGs. Tangentials are circles around the centre of rotation in the plane of rotation of the applicable airfoils.